Answer:
The first part of the question asks to evaluate the expression: 4C3 10 C3 4C3 10 C3.
To simplify, we can use the formula for combinations:
nCr = n! / (r! * (n - r)!)
where n is the total number of objects/events, and r is the number of objects/events we want to choose. The exclamation mark denotes the factorial function, which means that we multiply the given number by all positive integers less than itself.
Using this formula, we can simplify the expression as follows:
4C3 = 4! / (3! * (4 - 3)!) = 4 10C3 = 10! / (3! * (10 - 3)!) = 120 So, the expression becomes:
4 * 120 * 4 * 120 = 23,0400
Therefore, the simplified answer is 23,0400.
The second part of the question asks how many ways the textbook search committee can select 4 books out of 10 for further consideration.
This is another combination problem, where we want to choose 4 books out of a total of 10. Using the combination formula, we get:
10C4 = 10! / (4! * (10 - 4)!) = 210
Therefore, there are 210 different ways the committee can select 4 books out of 10 for further consideration.
Explanation: